Practical finite difference method for solving multi-dimensional black-Scholes model in fractal market

Jian Wang, Shuai Wen, Mengdie Yang and Wei Shao

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

Abstract: In this paper, we employ a practical finite difference method to research the multi-dimensional fractional Balck-Scholes model under one asset and three assets. In the case of one asset, we establish explicit scheme and Crank-Nicolson scheme to study the effect of different Hurst exponent (H) on numerical results and Greeks. With the increase of H, the numerical figures of the finite difference scheme also change. In addition, we also verify the effectiveness of Crank-Nicolson scheme in numerical solution of Greeks. We observe that when H=0.5, the results of Delta, Gamma and Theta are consistent with the accurate results. In the case of three assets, we use operator splitting method (OSM) and establish semi-implicit scheme. We hold that H will affect the numerical results and Greeks results in fractional Black-Scholes model. If the effect of H is not considered in option hedging, the result will deviate greatly from the actual result.

Keywords: European option; Fractional black-Scholes model; Hurst exponent (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001060

DOI: 10.1016/j.chaos.2022.111895

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